Question

The National Football League playoffs are just about to begin. Because of their great record in the regular season, the Colts get a bye in the first week of the playoffs. In the second week, they will play the winner of the game between the Ravens and the Patriots. A football expert estimates that the Ravens will beat the Patriots with probability 0.45. This same expert estimates that if the Colts play the Ravens, the mean and standard deviation of the point spread (Colts points minus Ravens points) will be 6.5 and 10.5, whereas if the Colts play the Patriots, the mean and standard deviation of the point spread (Colts points minus Patriots points) will be 3.5 and 12.5. Find the mean and standard deviation of the point spread (Colts points minus their opponent’s points) in the Colts game.